PRACTICE QUESTIONS FOR a CUBE PLUS b CUBE

a3+b3= (a+b) (a2-ab+b2)

Problem 1 :

Expand x3 + y

(A) (x + y) (x² - xy + y2)

(B) (x + y) (x² + xy + y²)

(C) (x - y) (x² - xy + y²)

Problem 2 :

Expand (2x)³ + (3y)³

(A)  (2x+3y) (4x²+ 6xy - 9y²)

(B)  (3x+2y) (9x² - 6xy + 9y²)

(C)  (2x+3y) (4x² - 6xy + 9y²)

Problem 3 :

Expand (3x)³ + y³

(A)  (3x + y) (9x² - 3xy + y²)

(B)  (3x - y) (9x² + 3 xy - y²)

(C)  (3x + y) (9x² + 3 xy + y²)

Problem 4 :

Expand (4x)³ + z³

 (A) (4x - z) (16x² + 4xz + z²)

 (B) (4x + z) (16x² + 4xz - z²)

 (C) (4x + z) (16 x² - 4xz + z²)

Problem 5 :

Expand (3p)³ + (2s)³

 (A) (3p - 2s) (9p² + 6 p s + 4s² )

 (B) (3p + 2s) (9p² - 6 ps - 4s²)

 (C) (3p + 2s) (9p² - 6 ps + 4s²)

Solutions for Practice Questions

Problem 1 :

Expand x3 + y

Solution :

Here a  =  x and b  =  y

(x3 + y3) = (x + y) (x2 - x y + y2)

Problem 2 :

Expand (2x)³ + (3y)³

Solution :

Here a = 2x and b = 3y

(2x)3 + (3y)3  =  (2x+3y) [(2x)2 - (2x)(3y) + (3y)2]

  =  (2x+3y) (4x2-6xy+9y2)

Problem 3 :

Expand (3x)³ + y³

Solution :

Here a  =  3x and b  =  y

(3x)3 + y3 = (3x+y) [(3x)2 - (3x)y + y2]

  =  (3x+y) (32x2-3xy+y2)

  =  (3x+y) (9x2-3xy+y2

Problem 4 :

Expand (4x)³ + z³

Solution :

Here a  =  4x and b  =  z

(4x)3 + z3  =  (4x+z) [(4x)2 - (4x)(z) + z2]

  =  (4x+z) (42x2 - 4xz + z2)

  =  (4x+z) (16x2 - 4xz + z2)

Problem 5 :

Expand (3p)³ + (2s)³

Solution :

Here a  =  3p and b  =  2s

(3p)3 + (2s)3  =  (3p+2s) [(3p)2 - (3p)(2s) + (2s)2]

  =  (3p+2s) (9p2 - 6ps + 4s2)

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